Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(289,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.s (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.04892052375\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 168) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 865.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.865 |
Dual form | 1008.2.s.f.289.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | 0.732294 | − | 0.680989i | \(-0.238450\pi\) |
−0.955901 | + | 0.293691i | \(0.905116\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.500000 | − | 2.59808i | −0.188982 | − | 0.981981i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.50000 | + | 2.59808i | −0.452267 | + | 0.783349i | −0.998526 | − | 0.0542666i | \(-0.982718\pi\) |
0.546259 | + | 0.837616i | \(0.316051\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.00000 | 1.10940 | 0.554700 | − | 0.832050i | \(-0.312833\pi\) | ||||
0.554700 | + | 0.832050i | \(0.312833\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.00000 | − | 3.46410i | −0.458831 | − | 0.794719i | 0.540068 | − | 0.841621i | \(-0.318398\pi\) |
−0.998899 | + | 0.0469020i | \(0.985065\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.00000 | − | 6.92820i | −0.834058 | − | 1.44463i | −0.894795 | − | 0.446476i | \(-0.852679\pi\) |
0.0607377 | − | 0.998154i | \(-0.480655\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.00000 | − | 3.46410i | 0.400000 | − | 0.692820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.00000 | 0.557086 | 0.278543 | − | 0.960424i | \(-0.410149\pi\) | ||||
0.278543 | + | 0.960424i | \(0.410149\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.50000 | + | 4.33013i | −0.449013 | + | 0.777714i | −0.998322 | − | 0.0579057i | \(-0.981558\pi\) |
0.549309 | + | 0.835619i | \(0.314891\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.00000 | + | 1.73205i | −0.338062 | + | 0.292770i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.00000 | − | 6.92820i | −0.657596 | − | 1.13899i | −0.981236 | − | 0.192809i | \(-0.938240\pi\) |
0.323640 | − | 0.946180i | \(-0.395093\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.00000 | −1.24939 | −0.624695 | − | 0.780869i | \(-0.714777\pi\) | ||||
−0.624695 | + | 0.780869i | \(0.714777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.00000 | −0.914991 | −0.457496 | − | 0.889212i | \(-0.651253\pi\) | ||||
−0.457496 | + | 0.889212i | \(0.651253\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.00000 | − | 8.66025i | −0.729325 | − | 1.26323i | −0.957169 | − | 0.289530i | \(-0.906501\pi\) |
0.227844 | − | 0.973698i | \(-0.426832\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.50000 | + | 2.59808i | −0.928571 | + | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.50000 | − | 7.79423i | 0.618123 | − | 1.07062i | −0.371706 | − | 0.928351i | \(-0.621227\pi\) |
0.989828 | − | 0.142269i | \(-0.0454398\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.00000 | 0.404520 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.50000 | − | 4.33013i | 0.325472 | − | 0.563735i | −0.656136 | − | 0.754643i | \(-0.727810\pi\) |
0.981608 | + | 0.190909i | \(0.0611434\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.00000 | + | 8.66025i | 0.640184 | + | 1.10883i | 0.985391 | + | 0.170305i | \(0.0544754\pi\) |
−0.345207 | + | 0.938527i | \(0.612191\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.00000 | − | 3.46410i | −0.248069 | − | 0.429669i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.00000 | − | 5.19615i | 0.366508 | − | 0.634811i | −0.622509 | − | 0.782613i | \(-0.713886\pi\) |
0.989017 | + | 0.147802i | \(0.0472198\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.0000 | 1.18678 | 0.593391 | − | 0.804914i | \(-0.297789\pi\) | ||||
0.593391 | + | 0.804914i | \(0.297789\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.00000 | + | 1.73205i | −0.117041 | + | 0.202721i | −0.918594 | − | 0.395203i | \(-0.870674\pi\) |
0.801553 | + | 0.597924i | \(0.204008\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.50000 | + | 2.59808i | 0.854704 | + | 0.296078i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.50000 | + | 9.52628i | 0.618798 | + | 1.07179i | 0.989705 | + | 0.143120i | \(0.0457135\pi\) |
−0.370907 | + | 0.928670i | \(0.620953\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.00000 | 0.768350 | 0.384175 | − | 0.923260i | \(-0.374486\pi\) | ||||
0.384175 | + | 0.923260i | \(0.374486\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.00000 | − | 15.5885i | −0.953998 | − | 1.65237i | −0.736644 | − | 0.676280i | \(-0.763591\pi\) |
−0.217354 | − | 0.976093i | \(-0.569742\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.00000 | − | 10.3923i | −0.209657 | − | 1.08941i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.00000 | + | 3.46410i | −0.205196 | + | 0.355409i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −17.0000 | −1.72609 | −0.863044 | − | 0.505128i | \(-0.831445\pi\) | ||||
−0.863044 | + | 0.505128i | \(0.831445\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.00000 | + | 1.73205i | −0.0995037 | + | 0.172345i | −0.911479 | − | 0.411346i | \(-0.865059\pi\) |
0.811976 | + | 0.583691i | \(0.198392\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.50000 | + | 9.52628i | 0.531705 | + | 0.920940i | 0.999315 | + | 0.0370053i | \(0.0117818\pi\) |
−0.467610 | + | 0.883935i | \(0.654885\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.00000 | − | 8.66025i | 0.478913 | − | 0.829502i | −0.520794 | − | 0.853682i | \(-0.674364\pi\) |
0.999708 | + | 0.0241802i | \(0.00769755\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.00000 | 0.752577 | 0.376288 | − | 0.926503i | \(-0.377200\pi\) | ||||
0.376288 | + | 0.926503i | \(0.377200\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.00000 | + | 6.92820i | −0.373002 | + | 0.646058i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | + | 1.73205i | 0.0909091 | + | 0.157459i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.00000 | −0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.00000 | 0.621150 | 0.310575 | − | 0.950549i | \(-0.399478\pi\) | ||||
0.310575 | + | 0.950549i | \(0.399478\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.50000 | − | 12.9904i | −0.655278 | − | 1.13497i | −0.981824 | − | 0.189794i | \(-0.939218\pi\) |
0.326546 | − | 0.945181i | \(-0.394115\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.00000 | + | 6.92820i | −0.693688 | + | 0.600751i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.00000 | + | 12.1244i | −0.598050 | + | 1.03585i | 0.395058 | + | 0.918656i | \(0.370724\pi\) |
−0.993109 | + | 0.117198i | \(0.962609\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 22.0000 | 1.86602 | 0.933008 | − | 0.359856i | \(-0.117174\pi\) | ||||
0.933008 | + | 0.359856i | \(0.117174\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.00000 | + | 10.3923i | −0.501745 | + | 0.869048i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.50000 | − | 2.59808i | −0.124568 | − | 0.215758i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.00000 | + | 15.5885i | 0.737309 | + | 1.27706i | 0.953703 | + | 0.300750i | \(0.0972370\pi\) |
−0.216394 | + | 0.976306i | \(0.569430\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.50000 | + | 4.33013i | −0.203447 | + | 0.352381i | −0.949637 | − | 0.313353i | \(-0.898548\pi\) |
0.746190 | + | 0.665733i | \(0.231881\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.00000 | 0.401610 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.00000 | − | 3.46410i | 0.159617 | − | 0.276465i | −0.775113 | − | 0.631822i | \(-0.782307\pi\) |
0.934731 | + | 0.355357i | \(0.115641\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −16.0000 | + | 13.8564i | −1.26098 | + | 1.09204i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.00000 | + | 6.92820i | 0.313304 | + | 0.542659i | 0.979076 | − | 0.203497i | \(-0.0652307\pi\) |
−0.665771 | + | 0.746156i | \(0.731897\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.00000 | −0.154765 | −0.0773823 | − | 0.997001i | \(-0.524656\pi\) | ||||
−0.0773823 | + | 0.997001i | \(0.524656\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.00000 | 0.230769 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.00000 | + | 1.73205i | 0.0760286 | + | 0.131685i | 0.901533 | − | 0.432710i | \(-0.142443\pi\) |
−0.825505 | + | 0.564396i | \(0.809109\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.0000 | − | 3.46410i | −0.755929 | − | 0.261861i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.00000 | + | 10.3923i | −0.448461 | + | 0.776757i | −0.998286 | − | 0.0585225i | \(-0.981361\pi\) |
0.549825 | + | 0.835280i | \(0.314694\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.00000 | + | 6.92820i | −0.294086 | + | 0.509372i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.00000 | + | 13.8564i | 0.578860 | + | 1.00261i | 0.995610 | + | 0.0935936i | \(0.0298354\pi\) |
−0.416751 | + | 0.909021i | \(0.636831\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.5000 | − | 23.3827i | 0.971751 | − | 1.68312i | 0.281487 | − | 0.959565i | \(-0.409172\pi\) |
0.690264 | − | 0.723558i | \(-0.257494\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 26.0000 | 1.85242 | 0.926212 | − | 0.377004i | \(-0.123046\pi\) | ||||
0.926212 | + | 0.377004i | \(0.123046\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.00000 | − | 10.3923i | 0.425329 | − | 0.736691i | −0.571122 | − | 0.820865i | \(-0.693492\pi\) |
0.996451 | + | 0.0841740i | \(0.0268252\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.50000 | − | 7.79423i | −0.105279 | − | 0.547048i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.00000 | + | 6.92820i | 0.279372 | + | 0.483887i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.0000 | 0.830057 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.00000 | −0.413057 | −0.206529 | − | 0.978441i | \(-0.566217\pi\) | ||||
−0.206529 | + | 0.978441i | \(0.566217\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.00000 | + | 5.19615i | 0.204598 | + | 0.354375i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.5000 | + | 4.33013i | 0.848555 | + | 0.293948i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.00000 | −0.0669650 | −0.0334825 | − | 0.999439i | \(-0.510660\pi\) | ||||
−0.0334825 | + | 0.999439i | \(0.510660\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.5000 | + | 18.1865i | −0.696909 | + | 1.20708i | 0.272623 | + | 0.962121i | \(0.412109\pi\) |
−0.969533 | + | 0.244962i | \(0.921225\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.00000 | + | 10.3923i | 0.396491 | + | 0.686743i | 0.993290 | − | 0.115648i | \(-0.0368944\pi\) |
−0.596799 | + | 0.802391i | \(0.703561\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.0000 | − | 20.7846i | −0.786146 | − | 1.36165i | −0.928312 | − | 0.371802i | \(-0.878740\pi\) |
0.142166 | − | 0.989843i | \(-0.454593\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.00000 | + | 8.66025i | −0.326164 | + | 0.564933i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.5000 | + | 19.9186i | −0.740780 | + | 1.28307i | 0.211360 | + | 0.977408i | \(0.432211\pi\) |
−0.952141 | + | 0.305661i | \(0.901123\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.50000 | + | 4.33013i | 0.351382 | + | 0.276642i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.00000 | − | 13.8564i | −0.509028 | − | 0.881662i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.0000 | 0.694314 | 0.347157 | − | 0.937807i | \(-0.387147\pi\) | ||||
0.347157 | + | 0.937807i | \(0.387147\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 24.0000 | 1.50887 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.00000 | + | 12.1244i | 0.436648 | + | 0.756297i | 0.997429 | − | 0.0716680i | \(-0.0228322\pi\) |
−0.560781 | + | 0.827964i | \(0.689499\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −16.0000 | + | 13.8564i | −0.994192 | + | 0.860995i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.00000 | − | 12.1244i | 0.431638 | − | 0.747620i | −0.565376 | − | 0.824833i | \(-0.691269\pi\) |
0.997015 | + | 0.0772134i | \(0.0246023\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.00000 | −0.552866 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.500000 | − | 0.866025i | 0.0304855 | − | 0.0528025i | −0.850380 | − | 0.526169i | \(-0.823628\pi\) |
0.880866 | + | 0.473366i | \(0.156961\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.50000 | − | 14.7224i | −0.516338 | − | 0.894324i | −0.999820 | − | 0.0189696i | \(-0.993961\pi\) |
0.483482 | − | 0.875354i | \(-0.339372\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.00000 | + | 10.3923i | 0.361814 | + | 0.626680i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.00000 | + | 6.92820i | −0.240337 | + | 0.416275i | −0.960810 | − | 0.277207i | \(-0.910591\pi\) |
0.720473 | + | 0.693482i | \(0.243925\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.00000 | −0.357930 | −0.178965 | − | 0.983855i | \(-0.557275\pi\) | ||||
−0.178965 | + | 0.983855i | \(0.557275\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.00000 | + | 15.5885i | −0.534994 | + | 0.926638i | 0.464169 | + | 0.885747i | \(0.346353\pi\) |
−0.999164 | + | 0.0408910i | \(0.986980\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.00000 | + | 20.7846i | 0.236113 | + | 1.22688i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.50000 | + | 14.7224i | 0.500000 | + | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.0000 | 1.10999 | 0.554996 | − | 0.831853i | \(-0.312720\pi\) | ||||
0.554996 | + | 0.831853i | \(0.312720\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.00000 | −0.291111 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −16.0000 | − | 27.7128i | −0.925304 | − | 1.60267i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.00000 | + | 15.5885i | 0.172917 | + | 0.898504i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.00000 | − | 8.66025i | 0.286299 | − | 0.495885i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.0000 | 0.913168 | 0.456584 | − | 0.889680i | \(-0.349073\pi\) | ||||
0.456584 | + | 0.889680i | \(0.349073\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.50000 | − | 7.79423i | −0.254355 | − | 0.440556i | 0.710365 | − | 0.703833i | \(-0.248530\pi\) |
−0.964720 | + | 0.263278i | \(0.915197\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.50000 | + | 11.2583i | 0.365076 | + | 0.632331i | 0.988788 | − | 0.149323i | \(-0.0477095\pi\) |
−0.623712 | + | 0.781654i | \(0.714376\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.50000 | + | 7.79423i | −0.251952 | + | 0.436393i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.00000 | − | 13.8564i | 0.443760 | − | 0.768615i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −20.0000 | + | 17.3205i | −1.10264 | + | 0.954911i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.00000 | + | 3.46410i | 0.109930 | + | 0.190404i | 0.915742 | − | 0.401768i | \(-0.131604\pi\) |
−0.805812 | + | 0.592172i | \(0.798271\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.00000 | −0.327815 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.0000 | −0.817102 | −0.408551 | − | 0.912735i | \(-0.633966\pi\) | ||||
−0.408551 | + | 0.912735i | \(0.633966\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.50000 | − | 12.9904i | −0.406148 | − | 0.703469i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0000 | + | 15.5885i | 0.539949 | + | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.0000 | − | 17.3205i | 0.536828 | − | 0.929814i | −0.462244 | − | 0.886753i | \(-0.652956\pi\) |
0.999072 | − | 0.0430610i | \(-0.0137110\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.00000 | 0.107058 | 0.0535288 | − | 0.998566i | \(-0.482953\pi\) | ||||
0.0535288 | + | 0.998566i | \(0.482953\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.00000 | − | 6.92820i | 0.212899 | − | 0.368751i | −0.739722 | − | 0.672913i | \(-0.765043\pi\) |
0.952620 | + | 0.304162i | \(0.0983763\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.00000 | − | 8.66025i | −0.265372 | − | 0.459639i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.00000 | − | 5.19615i | −0.158334 | − | 0.274242i | 0.775934 | − | 0.630814i | \(-0.217279\pi\) |
−0.934268 | + | 0.356572i | \(0.883946\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.50000 | − | 2.59808i | 0.0789474 | − | 0.136741i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.00000 | 0.104685 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.50000 | + | 6.06218i | −0.182699 | + | 0.316443i | −0.942799 | − | 0.333363i | \(-0.891817\pi\) |
0.760100 | + | 0.649806i | \(0.225150\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −22.5000 | − | 7.79423i | −1.16814 | − | 0.404656i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.00000 | − | 13.8564i | −0.414224 | − | 0.717458i | 0.581122 | − | 0.813816i | \(-0.302614\pi\) |
−0.995347 | + | 0.0963587i | \(0.969280\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.0000 | 0.618031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.0000 | 0.821865 | 0.410932 | − | 0.911666i | \(-0.365203\pi\) | ||||
0.410932 | + | 0.911666i | \(0.365203\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.00000 | − | 1.73205i | −0.0510976 | − | 0.0885037i | 0.839345 | − | 0.543599i | \(-0.182939\pi\) |
−0.890443 | + | 0.455095i | \(0.849605\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.50000 | − | 7.79423i | −0.0764471 | − | 0.397231i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.0000 | − | 22.5167i | 0.659126 | − | 1.14164i | −0.321716 | − | 0.946836i | \(-0.604260\pi\) |
0.980842 | − | 0.194804i | \(-0.0624070\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.50000 | − | 9.52628i | 0.276735 | − | 0.479319i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.0000 | − | 24.2487i | −0.702640 | − | 1.21701i | −0.967537 | − | 0.252731i | \(-0.918671\pi\) |
0.264897 | − | 0.964277i | \(-0.414662\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.00000 | − | 6.92820i | −0.199750 | − | 0.345978i | 0.748697 | − | 0.662912i | \(-0.230680\pi\) |
−0.948447 | + | 0.316934i | \(0.897346\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.0000 | + | 17.3205i | −0.498135 | + | 0.862796i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.0000 | 1.18964 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.50000 | + | 6.06218i | −0.173064 | + | 0.299755i | −0.939490 | − | 0.342578i | \(-0.888700\pi\) |
0.766426 | + | 0.642333i | \(0.222033\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.5000 | − | 4.33013i | −0.615085 | − | 0.213072i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.50000 | − | 6.06218i | −0.171808 | − | 0.297581i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.00000 | −0.292422 | −0.146211 | − | 0.989253i | \(-0.546708\pi\) | ||||
−0.146211 | + | 0.989253i | \(0.546708\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 20.0000 | − | 17.3205i | 0.967868 | − | 0.838198i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.00000 | − | 10.3923i | 0.289010 | − | 0.500580i | −0.684564 | − | 0.728953i | \(-0.740007\pi\) |
0.973574 | + | 0.228373i | \(0.0733406\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.00000 | −0.0961139 | −0.0480569 | − | 0.998845i | \(-0.515303\pi\) | ||||
−0.0480569 | + | 0.998845i | \(0.515303\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −16.0000 | + | 27.7128i | −0.765384 | + | 1.32568i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.50000 | − | 7.79423i | −0.214773 | − | 0.371998i | 0.738429 | − | 0.674331i | \(-0.235568\pi\) |
−0.953202 | + | 0.302333i | \(0.902235\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.500000 | + | 0.866025i | 0.0237557 | + | 0.0411461i | 0.877659 | − | 0.479286i | \(-0.159104\pi\) |
−0.853903 | + | 0.520432i | \(0.825771\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.00000 | + | 15.5885i | −0.426641 | + | 0.738964i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.00000 | −0.188772 | −0.0943858 | − | 0.995536i | \(-0.530089\pi\) | ||||
−0.0943858 | + | 0.995536i | \(0.530089\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.0000 | − | 20.7846i | 0.565058 | − | 0.978709i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.00000 | + | 6.92820i | −0.375046 | + | 0.324799i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.50000 | + | 14.7224i | 0.397613 | + | 0.688686i | 0.993431 | − | 0.114433i | \(-0.0365053\pi\) |
−0.595818 | + | 0.803120i | \(0.703172\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −30.0000 | −1.39724 | −0.698620 | − | 0.715493i | \(-0.746202\pi\) | ||||
−0.698620 | + | 0.715493i | \(0.746202\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.0000 | 0.743583 | 0.371792 | − | 0.928316i | \(-0.378744\pi\) | ||||
0.371792 | + | 0.928316i | \(0.378744\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.0000 | + | 24.2487i | 0.647843 | + | 1.12210i | 0.983637 | + | 0.180161i | \(0.0576619\pi\) |
−0.335794 | + | 0.941935i | \(0.609005\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.0000 | − | 5.19615i | −0.692636 | − | 0.239936i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.00000 | − | 15.5885i | 0.413820 | − | 0.716758i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16.0000 | −0.734130 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.00000 | + | 5.19615i | −0.137073 | + | 0.237418i | −0.926388 | − | 0.376571i | \(-0.877103\pi\) |
0.789314 | + | 0.613990i | \(0.210436\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.0000 | − | 27.7128i | −0.729537 | − | 1.26360i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.50000 | + | 14.7224i | 0.385965 | + | 0.668511i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.5000 | − | 32.0429i | 0.838315 | − | 1.45200i | −0.0529875 | − | 0.998595i | \(-0.516874\pi\) |
0.891303 | − | 0.453409i | \(-0.149792\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.00000 | −0.406164 | −0.203082 | − | 0.979162i | \(-0.565096\pi\) | ||||
−0.203082 | + | 0.979162i | \(0.565096\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.00000 | − | 25.9808i | −0.224281 | − | 1.16540i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.00000 | + | 8.66025i | 0.223831 | + | 0.387686i | 0.955968 | − | 0.293471i | \(-0.0948104\pi\) |
−0.732137 | + | 0.681157i | \(0.761477\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.0000 | −0.535054 | −0.267527 | − | 0.963550i | \(-0.586206\pi\) | ||||
−0.267527 | + | 0.963550i | \(0.586206\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.00000 | 0.0889988 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −19.5000 | − | 33.7750i | −0.864322 | − | 1.49705i | −0.867719 | − | 0.497056i | \(-0.834414\pi\) |
0.00339621 | − | 0.999994i | \(-0.498919\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.00000 | + | 1.73205i | 0.221187 | + | 0.0766214i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 30.0000 | 1.31940 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.00000 | + | 15.5885i | −0.394297 | + | 0.682943i | −0.993011 | − | 0.118020i | \(-0.962345\pi\) |
0.598714 | + | 0.800963i | \(0.295679\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.00000 | − | 10.3923i | −0.262362 | − | 0.454424i | 0.704507 | − | 0.709697i | \(-0.251168\pi\) |
−0.966869 | + | 0.255273i | \(0.917835\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.5000 | + | 35.5070i | −0.891304 | + | 1.54378i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −32.0000 | −1.38607 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.50000 | − | 9.52628i | 0.237786 | − | 0.411857i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.00000 | − | 20.7846i | 0.129219 | − | 0.895257i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.0000 | − | 29.4449i | −0.730887 | − | 1.26593i | −0.956504 | − | 0.291718i | \(-0.905773\pi\) |
0.225617 | − | 0.974216i | \(-0.427560\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10.0000 | −0.428353 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.00000 | 0.342055 | 0.171028 | − | 0.985266i | \(-0.445291\pi\) | ||||
0.171028 | + | 0.985266i | \(0.445291\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.00000 | − | 10.3923i | −0.255609 | − | 0.442727i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 22.0000 | − | 19.0526i | 0.935535 | − | 0.810197i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.50000 | − | 12.9904i | 0.317785 | − | 0.550420i | −0.662240 | − | 0.749291i | \(-0.730394\pi\) |
0.980026 | + | 0.198871i | \(0.0637276\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −24.0000 | −1.01509 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.5000 | + | 33.7750i | −0.821827 | + | 1.42345i | 0.0824933 | + | 0.996592i | \(0.473712\pi\) |
−0.904320 | + | 0.426855i | \(0.859622\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.00000 | − | 6.92820i | −0.168281 | − | 0.291472i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.00000 | + | 10.3923i | 0.251533 | + | 0.435668i | 0.963948 | − | 0.266090i | \(-0.0857319\pi\) |
−0.712415 | + | 0.701758i | \(0.752399\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.0000 | − | 19.0526i | 0.460336 | − | 0.797325i | −0.538642 | − | 0.842535i | \(-0.681062\pi\) |
0.998978 | + | 0.0452101i | \(0.0143957\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −32.0000 | −1.33449 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.5000 | − | 28.5788i | 0.686904 | − | 1.18975i | −0.285930 | − | 0.958250i | \(-0.592303\pi\) |
0.972834 | − | 0.231502i | \(-0.0743641\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.50000 | − | 18.1865i | −0.145204 | − | 0.754505i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.5000 | + | 23.3827i | 0.559113 | + | 0.968412i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 45.0000 | 1.85735 | 0.928674 | − | 0.370896i | \(-0.120949\pi\) | ||||
0.928674 | + | 0.370896i | \(0.120949\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.0000 | 0.824086 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21.0000 | − | 36.3731i | 0.858037 | − | 1.48616i | −0.0157622 | − | 0.999876i | \(-0.505017\pi\) |
0.873799 | − | 0.486287i | \(-0.161649\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.0000 | −0.530281 | −0.265141 | − | 0.964210i | \(-0.585418\pi\) | ||||
−0.265141 | + | 0.964210i | \(0.585418\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.00000 | − | 1.73205i | 0.0406558 | − | 0.0704179i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.50000 | + | 11.2583i | 0.263827 | + | 0.456962i | 0.967256 | − | 0.253804i | \(-0.0816819\pi\) |
−0.703429 | + | 0.710766i | \(0.748349\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −20.0000 | − | 34.6410i | −0.809113 | − | 1.40143i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.00000 | + | 6.92820i | −0.161558 | + | 0.279827i | −0.935428 | − | 0.353518i | \(-0.884985\pi\) |
0.773869 | + | 0.633345i | \(0.218319\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 30.0000 | 1.20775 | 0.603877 | − | 0.797077i | \(-0.293622\pi\) | ||||
0.603877 | + | 0.797077i | \(0.293622\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.00000 | − | 5.19615i | 0.120580 | − | 0.208851i | −0.799416 | − | 0.600777i | \(-0.794858\pi\) |
0.919997 | + | 0.391926i | \(0.128191\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −36.0000 | + | 31.1769i | −1.44231 | + | 1.24908i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.50000 | − | 9.52628i | −0.220000 | − | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.0000 | 0.437903 | 0.218952 | − | 0.975736i | \(-0.429736\pi\) | ||||
0.218952 | + | 0.975736i | \(0.429736\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.50000 | − | 6.06218i | −0.138893 | − | 0.240570i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −26.0000 | + | 10.3923i | −1.03016 | + | 0.411758i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.0000 | + | 19.0526i | −0.434474 | + | 0.752531i | −0.997253 | − | 0.0740768i | \(-0.976399\pi\) |
0.562779 | + | 0.826608i | \(0.309732\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −46.0000 | −1.81406 | −0.907031 | − | 0.421063i | \(-0.861657\pi\) | ||||
−0.907031 | + | 0.421063i | \(0.861657\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25.0000 | − | 43.3013i | 0.982851 | − | 1.70235i | 0.331731 | − | 0.943374i | \(-0.392367\pi\) |
0.651120 | − | 0.758975i | \(-0.274299\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.50000 | + | 12.9904i | 0.294401 | + | 0.509917i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.50000 | + | 12.9904i | 0.293498 | + | 0.508353i | 0.974634 | − | 0.223803i | \(-0.0718474\pi\) |
−0.681137 | + | 0.732156i | \(0.738514\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.50000 | + | 12.9904i | −0.293049 | + | 0.507576i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.0000 | 0.934907 | 0.467454 | − | 0.884018i | \(-0.345171\pi\) | ||||
0.467454 | + | 0.884018i | \(0.345171\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.0000 | + | 32.9090i | −0.739014 | + | 1.28001i | 0.213925 | + | 0.976850i | \(0.431375\pi\) |
−0.952940 | + | 0.303160i | \(0.901958\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 10.0000 | + | 3.46410i | 0.387783 | + | 0.134332i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.0000 | − | 20.7846i | −0.464642 | − | 0.804783i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −30.0000 | −1.15814 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.0000 | 1.11787 | 0.558934 | − | 0.829212i | \(-0.311211\pi\) | ||||
0.558934 | + | 0.829212i | \(0.311211\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.50000 | + | 16.4545i | 0.365115 | + | 0.632397i | 0.988795 | − | 0.149283i | \(-0.0476964\pi\) |
−0.623680 | + | 0.781680i | \(0.714363\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.50000 | + | 44.1673i | 0.326200 | + | 1.69499i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.50000 | + | 14.7224i | −0.325243 | + | 0.563338i | −0.981562 | − | 0.191146i | \(-0.938780\pi\) |
0.656318 | + | 0.754484i | \(0.272113\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.0000 | 0.534913 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 18.0000 | − | 31.1769i | 0.685745 | − | 1.18775i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −11.0000 | − | 19.0526i | −0.417254 | − | 0.722705i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.00000 | −0.188847 | −0.0944237 | − | 0.995532i | \(-0.530101\pi\) | ||||
−0.0944237 | + | 0.995532i | \(0.530101\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.0000 | + | 27.7128i | −0.603451 | + | 1.04521i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.00000 | + | 1.73205i | 0.188044 | + | 0.0651405i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.00000 | − | 5.19615i | −0.112667 | − | 0.195146i | 0.804178 | − | 0.594389i | \(-0.202606\pi\) |
−0.916845 | + | 0.399244i | \(0.869273\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 40.0000 | 1.49801 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.0000 | 0.448775 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17.0000 | + | 29.4449i | 0.633993 | + | 1.09811i | 0.986728 | + | 0.162385i | \(0.0519185\pi\) |
−0.352735 | + | 0.935723i | \(0.614748\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.00000 | − | 10.3923i | 0.222834 | − | 0.385961i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −47.0000 | −1.74313 | −0.871567 | − | 0.490277i | \(-0.836896\pi\) | ||||
−0.871567 | + | 0.490277i | \(0.836896\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.00000 | − | 12.1244i | −0.258551 | − | 0.447823i | 0.707303 | − | 0.706910i | \(-0.249912\pi\) |
−0.965854 | + | 0.259087i | \(0.916578\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.00000 | + | 15.5885i | 0.331519 | + | 0.574208i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.00000 | − | 8.66025i | 0.183928 | − | 0.318573i | −0.759287 | − | 0.650756i | \(-0.774452\pi\) |
0.943215 | + | 0.332184i | \(0.107785\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.0000 | 1.24734 | 0.623670 | − | 0.781688i | \(-0.285641\pi\) | ||||
0.623670 | + | 0.781688i | \(0.285641\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.00000 | − | 15.5885i | 0.329734 | − | 0.571117i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 22.0000 | − | 19.0526i | 0.803863 | − | 0.696165i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.5000 | − | 23.3827i | −0.492622 | − | 0.853246i | 0.507342 | − | 0.861745i | \(-0.330628\pi\) |
−0.999964 | + | 0.00849853i | \(0.997295\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.00000 | 0.181969 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.0000 | −0.363456 | −0.181728 | − | 0.983349i | \(-0.558169\pi\) | ||||
−0.181728 | + | 0.983349i | \(0.558169\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.00000 | − | 10.3923i | −0.217500 | − | 0.376721i | 0.736543 | − | 0.676391i | \(-0.236457\pi\) |
−0.954043 | + | 0.299670i | \(0.903123\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −25.0000 | − | 8.66025i | −0.905061 | − | 0.313522i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 10.0000 | − | 17.3205i | 0.361079 | − | 0.625407i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 37.0000 | 1.33425 | 0.667127 | − | 0.744944i | \(-0.267524\pi\) | ||||
0.667127 | + | 0.744944i | \(0.267524\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13.0000 | + | 22.5167i | −0.467578 | + | 0.809868i | −0.999314 | − | 0.0370420i | \(-0.988206\pi\) |
0.531736 | + | 0.846910i | \(0.321540\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.0000 | + | 17.3205i | 0.359211 | + | 0.622171i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 16.0000 | + | 27.7128i | 0.573259 | + | 0.992915i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.0000 | + | 25.9808i | −0.536742 | + | 0.929665i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.00000 | −0.142766 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.0000 | + | 19.0526i | −0.392108 | + | 0.679150i | −0.992727 | − | 0.120384i | \(-0.961587\pi\) |
0.600620 | + | 0.799535i | \(0.294921\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.00000 | − | 20.7846i | −0.142224 | − | 0.739016i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 20.0000 | + | 34.6410i | 0.710221 | + | 1.23014i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.00000 | −0.106265 | −0.0531327 | − | 0.998587i | \(-0.516921\pi\) | ||||
−0.0531327 | + | 0.998587i | \(0.516921\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.00000 | − | 5.19615i | −0.105868 | − | 0.183368i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 20.0000 | + | 6.92820i | 0.704907 | + | 0.244187i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8.00000 | + | 13.8564i | −0.281265 | + | 0.487165i | −0.971697 | − | 0.236232i | \(-0.924087\pi\) |
0.690432 | + | 0.723398i | \(0.257421\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.00000 | −0.0702295 | −0.0351147 | − | 0.999383i | \(-0.511180\pi\) | ||||
−0.0351147 | + | 0.999383i | \(0.511180\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.00000 | − | 6.92820i | 0.140114 | − | 0.242684i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.0000 | + | 20.7846i | 0.419827 | + | 0.727161i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.5000 | − | 33.7750i | −0.680555 | − | 1.17876i | −0.974812 | − | 0.223029i | \(-0.928406\pi\) |
0.294257 | − | 0.955726i | \(-0.404928\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.0000 | − | 27.7128i | 0.557725 | − | 0.966008i | −0.439961 | − | 0.898017i | \(-0.645008\pi\) |
0.997686 | − | 0.0679910i | \(-0.0216589\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −41.0000 | −1.42571 | −0.712855 | − | 0.701312i | \(-0.752598\pi\) | ||||
−0.712855 | + | 0.701312i | \(0.752598\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.00000 | − | 3.46410i | 0.0694629 | − | 0.120313i | −0.829202 | − | 0.558949i | \(-0.811205\pi\) |
0.898665 | + | 0.438636i | \(0.144538\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.00000 | + | 1.73205i | 0.0346064 | + | 0.0599401i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −24.0000 | −0.828572 | −0.414286 | − | 0.910147i | \(-0.635969\pi\) | ||||
−0.414286 | + | 0.910147i | \(0.635969\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.50000 | − | 2.59808i | −0.0516016 | − | 0.0893765i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.00000 | − | 3.46410i | 0.137442 | − | 0.119028i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −32.0000 | + | 55.4256i | −1.09695 | + | 1.89997i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.0000 | 0.479351 | 0.239675 | − | 0.970853i | \(-0.422959\pi\) | ||||
0.239675 | + | 0.970853i | \(0.422959\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.00000 | − | 12.1244i | 0.239115 | − | 0.414160i | −0.721345 | − | 0.692576i | \(-0.756476\pi\) |
0.960461 | + | 0.278416i | \(0.0898092\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.00000 | − | 12.1244i | −0.238837 | − | 0.413678i | 0.721544 | − | 0.692369i | \(-0.243433\pi\) |
−0.960381 | + | 0.278691i | \(0.910099\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −11.0000 | − | 19.0526i | −0.374444 | − | 0.648557i | 0.615799 | − | 0.787903i | \(-0.288833\pi\) |
−0.990244 | + | 0.139346i | \(0.955500\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.00000 | − | 1.73205i | 0.0340010 | − | 0.0588915i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −33.0000 | −1.11945 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.0000 | − | 20.7846i | 0.406604 | − | 0.704260i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.50000 | + | 23.3827i | 0.152128 | + | 0.790479i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.0000 | + | 27.7128i | 0.540282 | + | 0.935795i | 0.998888 | + | 0.0471555i | \(0.0150156\pi\) |
−0.458606 | + | 0.888640i | \(0.651651\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 54.0000 | 1.81931 | 0.909653 | − | 0.415369i | \(-0.136347\pi\) | ||||
0.909653 | + | 0.415369i | \(0.136347\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −40.0000 | −1.34611 | −0.673054 | − | 0.739594i | \(-0.735018\pi\) | ||||
−0.673054 | + | 0.739594i | \(0.735018\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 24.0000 | + | 41.5692i | 0.805841 | + | 1.39576i | 0.915722 | + | 0.401813i | \(0.131620\pi\) |
−0.109881 | + | 0.993945i | \(0.535047\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.50000 | − | 18.1865i | −0.117386 | − | 0.609957i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −20.0000 | + | 34.6410i | −0.669274 | + | 1.15922i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.0000 | 0.401116 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.50000 | + | 12.9904i | −0.250139 | + | 0.433253i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.00000 | + | 13.8564i | −0.265636 | + | 0.460094i | −0.967730 | − | 0.251990i | \(-0.918915\pi\) |
0.702094 | + | 0.712084i | \(0.252248\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.00000 | 0.198789 | 0.0993944 | − | 0.995048i | \(-0.468309\pi\) | ||||
0.0993944 | + | 0.995048i | \(0.468309\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.5000 | + | 18.1865i | −0.347499 | + | 0.601886i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −30.0000 | + | 25.9808i | −0.990687 | + | 0.857960i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.00000 | − | 13.8564i | −0.263896 | − | 0.457081i | 0.703378 | − | 0.710816i | \(-0.251674\pi\) |
−0.967274 | + | 0.253735i | \(0.918341\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 40.0000 | 1.31662 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −32.0000 | −1.05215 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 21.0000 | + | 36.3731i | 0.688988 | + | 1.19336i | 0.972166 | + | 0.234294i | \(0.0752779\pi\) |
−0.283178 | + | 0.959067i | \(0.591389\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 22.0000 | + | 17.3205i | 0.721021 | + | 0.567657i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.0000 | 0.620703 | 0.310351 | − | 0.950622i | \(-0.399553\pi\) | ||||
0.310351 | + | 0.950622i | \(0.399553\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.50000 | + | 11.2583i | −0.211894 | + | 0.367011i | −0.952307 | − | 0.305141i | \(-0.901296\pi\) |
0.740413 | + | 0.672152i | \(0.234630\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 32.0000 | + | 55.4256i | 1.04206 | + | 1.80491i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24.0000 | + | 41.5692i | 0.779895 | + | 1.35082i | 0.932002 | + | 0.362454i | \(0.118061\pi\) |
−0.152106 | + | 0.988364i | \(0.548606\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.00000 | + | 6.92820i | −0.129845 | + | 0.224899i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 38.0000 | 1.23094 | 0.615470 | − | 0.788160i | \(-0.288966\pi\) | ||||
0.615470 | + | 0.788160i | \(0.288966\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.00000 | − | 13.8564i | 0.258874 | − | 0.448383i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 35.0000 | + | 12.1244i | 1.13021 | + | 0.391516i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.00000 | + | 5.19615i | 0.0967742 | + | 0.167618i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −27.0000 | −0.869161 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.00000 | −0.0964735 | −0.0482367 | − | 0.998836i | \(-0.515360\pi\) | ||||
−0.0482367 | + | 0.998836i | \(0.515360\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.5000 | − | 21.6506i | −0.401144 | − | 0.694802i | 0.592720 | − | 0.805408i | \(-0.298054\pi\) |
−0.993864 | + | 0.110607i | \(0.964721\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.0000 | − | 57.1577i | −0.352644 | − | 1.83239i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −11.0000 | + | 19.0526i | −0.351921 | + | 0.609545i | −0.986586 | − | 0.163242i | \(-0.947805\pi\) |
0.634665 | + | 0.772787i | \(0.281138\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 54.0000 | 1.72585 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −22.0000 | + | 38.1051i | −0.701691 | + | 1.21536i | 0.266181 | + | 0.963923i | \(0.414238\pi\) |
−0.967872 | + | 0.251442i | \(0.919095\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13.0000 | − | 22.5167i | −0.414214 | − | 0.717440i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24.0000 | + | 41.5692i | 0.763156 | + | 1.32182i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.50000 | − | 12.9904i | 0.238245 | − | 0.412653i | −0.721966 | − | 0.691929i | \(-0.756761\pi\) |
0.960211 | + | 0.279276i | \(0.0900944\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12.0000 | −0.380426 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.0000 | − | 22.5167i | 0.411714 | − | 0.713110i | −0.583363 | − | 0.812211i | \(-0.698264\pi\) |
0.995077 | + | 0.0991016i | \(0.0315969\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1008.2.s.f.865.1 | 2 | ||
3.2 | odd | 2 | 336.2.q.e.193.1 | 2 | |||
4.3 | odd | 2 | 504.2.s.d.361.1 | 2 | |||
7.2 | even | 3 | inner | 1008.2.s.f.289.1 | 2 | ||
7.3 | odd | 6 | 7056.2.a.t.1.1 | 1 | |||
7.4 | even | 3 | 7056.2.a.bk.1.1 | 1 | |||
12.11 | even | 2 | 168.2.q.a.25.1 | ✓ | 2 | ||
21.2 | odd | 6 | 336.2.q.e.289.1 | 2 | |||
21.5 | even | 6 | 2352.2.q.f.961.1 | 2 | |||
21.11 | odd | 6 | 2352.2.a.g.1.1 | 1 | |||
21.17 | even | 6 | 2352.2.a.u.1.1 | 1 | |||
21.20 | even | 2 | 2352.2.q.f.1537.1 | 2 | |||
24.5 | odd | 2 | 1344.2.q.d.193.1 | 2 | |||
24.11 | even | 2 | 1344.2.q.o.193.1 | 2 | |||
28.3 | even | 6 | 3528.2.a.i.1.1 | 1 | |||
28.11 | odd | 6 | 3528.2.a.q.1.1 | 1 | |||
28.19 | even | 6 | 3528.2.s.p.3313.1 | 2 | |||
28.23 | odd | 6 | 504.2.s.d.289.1 | 2 | |||
28.27 | even | 2 | 3528.2.s.p.361.1 | 2 | |||
84.11 | even | 6 | 1176.2.a.g.1.1 | 1 | |||
84.23 | even | 6 | 168.2.q.a.121.1 | yes | 2 | ||
84.47 | odd | 6 | 1176.2.q.g.961.1 | 2 | |||
84.59 | odd | 6 | 1176.2.a.c.1.1 | 1 | |||
84.83 | odd | 2 | 1176.2.q.g.361.1 | 2 | |||
168.11 | even | 6 | 9408.2.a.ba.1.1 | 1 | |||
168.53 | odd | 6 | 9408.2.a.cq.1.1 | 1 | |||
168.59 | odd | 6 | 9408.2.a.cf.1.1 | 1 | |||
168.101 | even | 6 | 9408.2.a.p.1.1 | 1 | |||
168.107 | even | 6 | 1344.2.q.o.961.1 | 2 | |||
168.149 | odd | 6 | 1344.2.q.d.961.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.2.q.a.25.1 | ✓ | 2 | 12.11 | even | 2 | ||
168.2.q.a.121.1 | yes | 2 | 84.23 | even | 6 | ||
336.2.q.e.193.1 | 2 | 3.2 | odd | 2 | |||
336.2.q.e.289.1 | 2 | 21.2 | odd | 6 | |||
504.2.s.d.289.1 | 2 | 28.23 | odd | 6 | |||
504.2.s.d.361.1 | 2 | 4.3 | odd | 2 | |||
1008.2.s.f.289.1 | 2 | 7.2 | even | 3 | inner | ||
1008.2.s.f.865.1 | 2 | 1.1 | even | 1 | trivial | ||
1176.2.a.c.1.1 | 1 | 84.59 | odd | 6 | |||
1176.2.a.g.1.1 | 1 | 84.11 | even | 6 | |||
1176.2.q.g.361.1 | 2 | 84.83 | odd | 2 | |||
1176.2.q.g.961.1 | 2 | 84.47 | odd | 6 | |||
1344.2.q.d.193.1 | 2 | 24.5 | odd | 2 | |||
1344.2.q.d.961.1 | 2 | 168.149 | odd | 6 | |||
1344.2.q.o.193.1 | 2 | 24.11 | even | 2 | |||
1344.2.q.o.961.1 | 2 | 168.107 | even | 6 | |||
2352.2.a.g.1.1 | 1 | 21.11 | odd | 6 | |||
2352.2.a.u.1.1 | 1 | 21.17 | even | 6 | |||
2352.2.q.f.961.1 | 2 | 21.5 | even | 6 | |||
2352.2.q.f.1537.1 | 2 | 21.20 | even | 2 | |||
3528.2.a.i.1.1 | 1 | 28.3 | even | 6 | |||
3528.2.a.q.1.1 | 1 | 28.11 | odd | 6 | |||
3528.2.s.p.361.1 | 2 | 28.27 | even | 2 | |||
3528.2.s.p.3313.1 | 2 | 28.19 | even | 6 | |||
7056.2.a.t.1.1 | 1 | 7.3 | odd | 6 | |||
7056.2.a.bk.1.1 | 1 | 7.4 | even | 3 | |||
9408.2.a.p.1.1 | 1 | 168.101 | even | 6 | |||
9408.2.a.ba.1.1 | 1 | 168.11 | even | 6 | |||
9408.2.a.cf.1.1 | 1 | 168.59 | odd | 6 | |||
9408.2.a.cq.1.1 | 1 | 168.53 | odd | 6 |